Rocket Equation Approximation in matlab

Sorry this may end up being a bit long but I'm stuck on a question and unsure of where to go from where I am. The question is as follows:

_Design and implement a program that can be used to calculate the speed and position of a rocket whose motion is expressed through the differential equation contained in the reading material.

Use an explicit method, see worksheet 2, to approximate the right hand side of the equation. Your submission should include:

a. A program design using either pseudo code or a flowchart. I am looking only for the design of the master program and a design of the main control within the solver function. [2 Marks]

b. A Matlab implementation of the design. [4 Marks]

c. A plot that shows a test of your implementation compared to the solution of Tsiolkovsky’s rocket equations. Use data from the tables below but set G and CD to zero. [2 Marks]

d. A plot of how the velocity changes in the first 1000 s of the rocket’s flight according to the solution of (1) using the parameters stated below. Comment on how the last two terms in (1) have affected the velocity at the end of the fuel burn stage. [2 Marks]

Note that the parts to the question match the normal stages of program development. Design, implement, test and investigate (this is also called research) are what any program developer should do._

Parameters to use are as follows: Fixed

Symbol Description Value

G the universal gravitational constant 6.67408 10-11 m3.kg-1.s-2

M Mass of the earth 5.9722 1024 kg

R Radius of the earth 6371 km

A Area of the rocket 75 m2

me Empty mass of the rocket 54000 kg

m0 Initial mass of the rocket 894000 kg

ve Exhaust gas speed 4500 m.s-1

dm/dt Rate of change of mass, whilst there is fuel left 5000 kg.s-1 Rate of change of mass after all fuel has been used 0 kg.s-1

You should assume density is a function of altitude, h = r – R, and the function you should use is: ρ=1.225*10^(-3h/50000)

Initial values (At t=0) Symbol Description Value

V speed 0 m.s-1

r radius R

h altitude 0 km

So i cant do part b properly as I want to use part b to make the pseudocode and was wondering if anyone could help?

Thanks

[David Oshidero]

also I forgot but this is my code

clc

%Define Constants
G = 6.67408*10^-11;
M = 5.9722*10^24;
%R is radius of earth - initial radius
%A is area of rocket
%me mass of empty rocket
%m0 initial mass of rocke%ve is exhaust gas speed
%dm/dt rate of change of mass
%Cd is coefficient of drag
R = 6371*10^3;
A = 75;
Cd = 0.4;
me = 54000;
m0 = 894000;
ve = 4500;

% computing air density
h = r(t)-R;
h = h(t);
p = 1.225*10^(-3*h/50000);

if p>=0
  r(t) = r(t-dt)+dt*0.5*(V(t)+V(t-dt));
end

[Rik]

Comment posted as answer by NABEEL ABED:

Dear David Oshidero

I am interested to know the code of this problem.... Have you solved it ??

If yes, could you please share the code with me ??

Thank you very much

[Rik]

@Nabeel: even if he did find a solution, he shouldn't simply share it, because that would be cheating.